An alternating current is given by The r.m.s. current will be [2025]

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Solution

Q.
An alternating current is given by

$I = I_{A} \sin ω t + I_{B} \cos ω t$

The r.m.s. current will be [2025]

1 $\sqrt{I_{A}^{2} + I_{B}^{2}}$

2 $\frac{\sqrt{I_{A}^{2} + I_{B}^{2}}}{2}$

3 $\sqrt{\frac{I_{A}^{2} + I_{B}^{2}}{2}}$

4 $\frac{| I_{A} + I_{B} |}{\sqrt{2}}$

Ans.
(3)

$I = I_{A} \sin ω t + I_{B} \cos ω t$

So, $I_{RMS} = \sqrt{\frac{I_{A}^{2} + I_{B}^{2}}{2}}$

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Solution

Q. An alternating current is given by I=IA sin ωt+IB cos ωt The r.m.s. current will be [2025]

1 IA2+IB2

2 IA2+IB22

3 IA2+IB22

4 |IA+IB|2

Ans. (3) I=IA sin ωt+IB cos ωt So, IRMS=IA2+IB22

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Q.
An alternating current is given by

$I = I_{A} \sin ω t + I_{B} \cos ω t$

The r.m.s. current will be [2025]

1 $\sqrt{I_{A}^{2} + I_{B}^{2}}$

2 $\frac{\sqrt{I_{A}^{2} + I_{B}^{2}}}{2}$

3 $\sqrt{\frac{I_{A}^{2} + I_{B}^{2}}{2}}$

4 $\frac{| I_{A} + I_{B} |}{\sqrt{2}}$

Ans.
(3)

$I = I_{A} \sin ω t + I_{B} \cos ω t$

So, $I_{RMS} = \sqrt{\frac{I_{A}^{2} + I_{B}^{2}}{2}}$